Pandas Profiling Report

Dataset statistics

Number of variables	10
Number of observations	72157
Missing cells	0
Missing cells (%)	0.0%
Duplicate rows	1
Duplicate rows (%)	< 0.1%
Total size in memory	5.5 MiB
Average record size in memory	80.0 B

Variable types

Numeric	10

Alerts

Dataset has 1 (< 0.1%) duplicate rows	Duplicates
`x2` is highly correlated with `x7`	High correlation
`x7` is highly correlated with `x2`	High correlation
`x2` is highly correlated with `x7`	High correlation
`x7` is highly correlated with `x2`	High correlation
`x2` is highly correlated with `x7`	High correlation
`x7` is highly correlated with `x2`	High correlation
`x1` is highly correlated with `x2`	High correlation
`x2` is highly correlated with `x1` and 3 other fields	High correlation
`x3` is highly correlated with `x7` and 1 other fields	High correlation
`x4` is highly correlated with `x2`	High correlation
`x7` is highly correlated with `x2` and 4 other fields	High correlation
`x8` is highly correlated with `x7` and 2 other fields	High correlation
`x9` is highly correlated with `x7` and 2 other fields	High correlation
`x10` is highly correlated with `x2` and 4 other fields	High correlation

Reproduction

Analysis started	2022-03-01 05:39:29.475968
Analysis finished	2022-03-01 05:39:47.663605
Duration	18.19 seconds
Software version	pandas-profiling v3.1.0
Download configuration	config.json

x1
Real number (ℝ)

HIGH CORRELATION

Distinct	3790
Distinct (%)	5.3%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%
Mean	-0.03898929373

Minimum	-2.9756
Maximum	2.4785
Zeros	88
Zeros (%)	0.1%
Negative	40592
Negative (%)	56.3%
Memory size	563.9 KiB

Quantile statistics

Minimum	-2.9756
5-th percentile	-0.4233
Q1	-0.1694
median	-0.0283
Q3	0.0889
95-th percentile	0.3267
Maximum	2.4785
Range	5.4541
Interquartile range (IQR)	0.2583

Descriptive statistics

Standard deviation	0.2488961446
Coefficient of variation (CV)	-6.383704877
Kurtosis	5.488000297
Mean	-0.03898929373
Median Absolute Deviation (MAD)	0.1275
Skewness	0.02418344853
Sum	-2813.350468
Variance	0.06194929077
Monotonicity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
-0.0347	104	0.1%
-0.0146	102	0.1%
0.0083	100	0.1%
0.0132	100	0.1%
0.0244	99	0.1%
0.0283	99	0.1%
-0.0195	98	0.1%
-0.0396	98	0.1%
-0.0415	97	0.1%
0.0469	96	0.1%
Other values (3780)	71164	98.6%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
-2.9756	1	< 0.1%
-2.3838	1	< 0.1%
-2.3364	1	< 0.1%
-2.2588	1	< 0.1%
-2.0586	1	< 0.1%
-2.0029	1	< 0.1%
-1.9409	1	< 0.1%
-1.8813	1	< 0.1%
-1.8521	1	< 0.1%
-1.8496	1	< 0.1%

Value	Count	Frequency (%)
2.4785	1	< 0.1%
2.4224	1	< 0.1%
2.2813	1	< 0.1%
2.0928	1	< 0.1%
2.084	1	< 0.1%
2.0596	1	< 0.1%
2.0527	1	< 0.1%
2.0127	1	< 0.1%
1.9429	1	< 0.1%
1.8579	1	< 0.1%

x2
Real number (ℝ)

HIGH CORRELATION
HIGH CORRELATION
HIGH CORRELATION
HIGH CORRELATION

Distinct	9638
Distinct (%)	13.4%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%
Mean	0.2366937245

Minimum	-10.5142
Maximum	7.5649
Zeros	10
Zeros (%)	< 0.1%
Negative	26896
Negative (%)	37.3%
Memory size	563.9 KiB

Quantile statistics

Minimum	-10.5142
5-th percentile	-1.3082
Q1	-0.5293
median	0.355
Q3	0.958
95-th percentile	1.5523
Maximum	7.5649
Range	18.0791
Interquartile range (IQR)	1.4873

Descriptive statistics

Standard deviation	1.017707897
Coefficient of variation (CV)	4.299682633
Kurtosis	4.879598735
Mean	0.2366937245
Median Absolute Deviation (MAD)	0.7036
Skewness	-0.5529297618
Sum	17079.10908
Variance	1.035729363
Monotonicity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0.8926	28	< 0.1%
0.8853	27	< 0.1%
1.042	27	< 0.1%
0.875	27	< 0.1%
1.0488	27	< 0.1%
0.9077	27	< 0.1%
0.3604	26	< 0.1%
0.9282	26	< 0.1%
0.5981	26	< 0.1%
0.897	26	< 0.1%
Other values (9628)	71890	99.6%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
-10.5142	1	< 0.1%
-10.3706	1	< 0.1%
-10.2734	1	< 0.1%
-10.1777	1	< 0.1%
-10.1445	1	< 0.1%
-10.0332	1	< 0.1%
-9.6143	1	< 0.1%
-9.563	1	< 0.1%
-9.4858	1	< 0.1%
-9.2837	1	< 0.1%

Value	Count	Frequency (%)
7.5649	1	< 0.1%
7.4106	1	< 0.1%
7.3711	1	< 0.1%
7.3203	1	< 0.1%
7.0688	1	< 0.1%
6.9346	1	< 0.1%
6.8618	1	< 0.1%
6.7349	1	< 0.1%
6.729	1	< 0.1%
6.6699	1	< 0.1%

x3
Real number (ℝ)

HIGH CORRELATION

Distinct	8041
Distinct (%)	11.1%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%
Mean	0.8122275425

Minimum	-4.4111
Maximum	3.7603
Zeros	20
Zeros (%)	< 0.1%
Negative	21753
Negative (%)	30.1%
Memory size	563.9 KiB

Quantile statistics

Minimum	-4.4111
5-th percentile	-0.5792
Q1	-0.0757
median	1.0249
Q3	1.7212
95-th percentile	2.0527
Maximum	3.7603
Range	8.1714
Interquartile range (IQR)	1.7969

Descriptive statistics

Standard deviation	0.9731434416
Coefficient of variation (CV)	1.198116772
Kurtosis	-0.9552484626
Mean	0.8122275425
Median Absolute Deviation (MAD)	0.8657
Skewness	-0.2668906721
Sum	58607.90278
Variance	0.9470081579
Monotonicity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
1.7715	42	0.1%
-0.1519	41	0.1%
-0.0728	41	0.1%
1.9092	40	0.1%
1.8027	39	0.1%
1.8003	39	0.1%
1.8125	38	0.1%
1.853	38	0.1%
1.7144	38	0.1%
1.7759	38	0.1%
Other values (8031)	71763	99.5%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
-4.4111	1	< 0.1%
-3.9805	1	< 0.1%
-3.9395	1	< 0.1%
-3.8804	1	< 0.1%
-3.8691	1	< 0.1%
-3.7832	1	< 0.1%
-3.7622	1	< 0.1%
-3.7393	1	< 0.1%
-3.6436	1	< 0.1%
-3.6084	1	< 0.1%

Value	Count	Frequency (%)
3.7603	1	< 0.1%
3.4565	1	< 0.1%
3.4512	1	< 0.1%
3.4199	1	< 0.1%
3.4175	1	< 0.1%
3.3716	1	< 0.1%
3.3159	1	< 0.1%
3.3081	1	< 0.1%
3.2573	1	< 0.1%
3.2529	1	< 0.1%

x4
Real number (ℝ)

HIGH CORRELATION

Distinct	7806
Distinct (%)	10.8%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%
Mean	0.3161115295

Minimum	-1411.499
Maximum	1173.1567
Zeros	337
Zeros (%)	0.5%
Negative	34961
Negative (%)	48.5%
Memory size	563.9 KiB

Quantile statistics

Minimum	-1411.499
5-th percentile	-98.3276
Q1	-21.1792
median	0.8545
Q3	21.4233
95-th percentile	109.8755
Maximum	1173.1567
Range	2584.6557
Interquartile range (IQR)	42.6025

Descriptive statistics

Standard deviation	86.37854929
Coefficient of variation (CV)	273.2533971
Kurtosis	30.50387693
Mean	0.3161115295
Median Absolute Deviation (MAD)	21.3013
Skewness	-1.564935663
Sum	22809.65963
Variance	7461.253778
Monotonicity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0	337	0.5%
0.6714	87	0.1%
-0.3662	87	0.1%
2.7466	87	0.1%
0.9766	85	0.1%
2.9907	83	0.1%
-0.9766	82	0.1%
2.3193	81	0.1%
1.8311	80	0.1%
1.1597	80	0.1%
Other values (7796)	71068	98.5%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
-1411.499	1	< 0.1%
-1397.7051	1	< 0.1%
-1341.5527	1	< 0.1%
-1317.3218	1	< 0.1%
-1275.6958	1	< 0.1%
-1243.5303	1	< 0.1%
-1241.333	1	< 0.1%
-1165.6494	1	< 0.1%
-1158.4473	1	< 0.1%
-1139.2822	1	< 0.1%

Value	Count	Frequency (%)
1173.1567	1	< 0.1%
1092.1021	1	< 0.1%
869.873	1	< 0.1%
854.126	1	< 0.1%
778.9307	1	< 0.1%
752.5024	1	< 0.1%
739.8071	1	< 0.1%
719.6045	1	< 0.1%
713.0127	1	< 0.1%
710.8154	1	< 0.1%

x5
Real number (ℝ)

Distinct	4978
Distinct (%)	6.9%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%
Mean	0.502638914

Minimum	-464.0503
Maximum	456.9702
Zeros	307
Zeros (%)	0.4%
Negative	36224
Negative (%)	50.2%
Memory size	563.9 KiB

Quantile statistics

Minimum	-464.0503
5-th percentile	-62.0117
Q1	-20.1416
median	-0.3052
Q3	20.5688
95-th percentile	65.6738
Maximum	456.9702
Range	921.0205
Interquartile range (IQR)	40.7104

Descriptive statistics

Standard deviation	43.09454618
Coefficient of variation (CV)	85.73658939
Kurtosis	7.68604623
Mean	0.502638914
Median Absolute Deviation (MAD)	20.2637
Skewness	0.127333299
Sum	36268.91612
Variance	1857.139911
Monotonicity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0	307	0.4%
-4.7607	86	0.1%
4.7607	80	0.1%
0.1831	79	0.1%
4.5776	78	0.1%
1.8311	77	0.1%
-0.5493	77	0.1%
4.0283	77	0.1%
-1.1597	77	0.1%
2.4414	77	0.1%
Other values (4968)	71142	98.6%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
-464.0503	1	< 0.1%
-452.6978	1	< 0.1%
-390.0757	1	< 0.1%
-381.5918	1	< 0.1%
-371.1548	1	< 0.1%
-348.5107	1	< 0.1%
-344.4824	1	< 0.1%
-341.2476	1	< 0.1%
-336.853	1	< 0.1%
-335.083	1	< 0.1%

Value	Count	Frequency (%)
456.9702	1	< 0.1%
421.7529	1	< 0.1%
420.7764	1	< 0.1%
409.4849	1	< 0.1%
405.3345	1	< 0.1%
400.6348	1	< 0.1%
392.8223	1	< 0.1%
383.4229	1	< 0.1%
382.9346	1	< 0.1%
365.2344	1	< 0.1%

x6
Real number (ℝ)

Distinct	3463
Distinct (%)	4.8%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%
Mean	0.04412119356

Minimum	-273.0103
Maximum	651.3062
Zeros	533
Zeros (%)	0.7%
Negative	35851
Negative (%)	49.7%
Memory size	563.9 KiB

Quantile statistics

Minimum	-273.0103
5-th percentile	-34.9731
Q1	-11.4746
median	0
Q3	11.3525
95-th percentile	34.8511
Maximum	651.3062
Range	924.3165
Interquartile range (IQR)	22.8271

Descriptive statistics

Standard deviation	27.94899448
Coefficient of variation (CV)	633.4596195
Kurtosis	57.04156399
Mean	0.04412119356
Median Absolute Deviation (MAD)	11.4136
Skewness	2.771312533
Sum	3183.652964
Variance	781.1462927
Monotonicity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0	533	0.7%
-1.77	135	0.2%
0.9766	134	0.2%
0.5493	133	0.2%
-1.2817	131	0.2%
-0.9155	130	0.2%
-3.7842	129	0.2%
-3.9673	128	0.2%
1.5869	127	0.2%
0.3662	127	0.2%
Other values (3453)	70450	97.6%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
-273.0103	1	< 0.1%
-270.752	1	< 0.1%
-267.6392	1	< 0.1%
-265.1367	1	< 0.1%
-243.9575	1	< 0.1%
-238.0981	1	< 0.1%
-237.0605	1	< 0.1%
-229.4312	1	< 0.1%
-222.9004	1	< 0.1%
-221.8628	1	< 0.1%

Value	Count	Frequency (%)
651.3062	1	< 0.1%
645.2026	1	< 0.1%
628.6011	1	< 0.1%
625.9155	1	< 0.1%
601.8677	1	< 0.1%
583.252	1	< 0.1%
564.5752	1	< 0.1%
558.7158	1	< 0.1%
550.5981	1	< 0.1%
529.1138	1	< 0.1%

x7
Real number (ℝ)

HIGH CORRELATION
HIGH CORRELATION
HIGH CORRELATION
HIGH CORRELATION

Distinct	33020
Distinct (%)	45.8%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%
Mean	22.46346776

Minimum	-180
Maximum	179.9945
Zeros	7
Zeros (%)	< 0.1%
Negative	29379
Negative (%)	40.7%
Memory size	563.9 KiB

Quantile statistics

Minimum	-180
5-th percentile	-119.016
Q1	-28.5645
median	17.309
Q3	90.7965
95-th percentile	149.8403
Maximum	179.9945
Range	359.9945
Interquartile range (IQR)	119.361

Descriptive statistics

Standard deviation	79.36284172
Coefficient of variation (CV)	3.53297374
Kurtosis	-0.1742541562
Mean	22.46346776
Median Absolute Deviation (MAD)	57.2278
Skewness	-0.3286215476
Sum	1620896.443
Variance	6298.460646
Monotonicity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
-27.301	14	< 0.1%
-25.296	12	< 0.1%
102.063	12	< 0.1%
102.2388	11	< 0.1%
103.9801	11	< 0.1%
38.952	11	< 0.1%
103.9581	11	< 0.1%
-2.8894	11	< 0.1%
103.4747	11	< 0.1%
101.4148	11	< 0.1%
Other values (33010)	72042	99.8%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
-180	1	< 0.1%
-179.978	1	< 0.1%
-179.967	1	< 0.1%
-179.9561	2	< 0.1%
-179.9451	1	< 0.1%
-179.9396	1	< 0.1%
-179.9341	1	< 0.1%
-179.9286	2	< 0.1%
-179.9231	2	< 0.1%
-179.9176	1	< 0.1%

Value	Count	Frequency (%)
179.9945	1	< 0.1%
179.989	1	< 0.1%
179.9835	1	< 0.1%
179.978	1	< 0.1%
179.9561	1	< 0.1%
179.9506	1	< 0.1%
179.9396	2	< 0.1%
179.9286	1	< 0.1%
179.9176	1	< 0.1%
179.8956	3	< 0.1%

x8
Real number (ℝ)

HIGH CORRELATION

Distinct	16153
Distinct (%)	22.4%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%
Mean	0.8708897857

Minimum	-132.7863
Maximum	96.6577
Zeros	70
Zeros (%)	0.1%
Negative	34307
Negative (%)	47.5%
Memory size	563.9 KiB

Quantile statistics

Minimum	-132.7863
5-th percentile	-28.3063
Q1	-4.5264
median	0.3186
Q3	6.795
95-th percentile	37.7501
Maximum	96.6577
Range	229.444
Interquartile range (IQR)	11.3214

Descriptive statistics

Standard deviation	23.34626395
Coefficient of variation (CV)	26.80736913
Kurtosis	5.634309704
Mean	0.8708897857
Median Absolute Deviation (MAD)	5.5811
Skewness	-0.5519484465
Sum	62840.79427
Variance	545.0480406
Monotonicity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0	70	0.1%
1.192	43	0.1%
-0.0824	42	0.1%
-0.1373	41	0.1%
0.1593	41	0.1%
0.0714	41	0.1%
-0.3516	40	0.1%
0.3735	39	0.1%
0.1318	38	0.1%
0.8295	38	0.1%
Other values (16143)	71724	99.4%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
-132.7863	1	< 0.1%
-132.4292	1	< 0.1%
-131.9897	1	< 0.1%
-131.5009	1	< 0.1%
-131.0065	1	< 0.1%
-130.545	1	< 0.1%
-130.144	1	< 0.1%
-129.776	1	< 0.1%
-129.4189	1	< 0.1%
-128.996	1	< 0.1%

Value	Count	Frequency (%)
96.6577	1	< 0.1%
96.6193	1	< 0.1%
96.5424	1	< 0.1%
96.4929	1	< 0.1%
96.427	1	< 0.1%
96.3831	1	< 0.1%
96.3062	1	< 0.1%
96.2128	1	< 0.1%
96.1963	1	< 0.1%
95.9711	1	< 0.1%

x9
Real number (ℝ)

HIGH CORRELATION

Distinct	20268
Distinct (%)	28.1%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%
Mean	-9.743400374

Minimum	-180
Maximum	179.989
Zeros	43
Zeros (%)	0.1%
Negative	38181
Negative (%)	52.9%
Memory size	563.9 KiB

Quantile statistics

Minimum	-180
5-th percentile	-117.3812
Q1	-9.7064
median	-0.6537
Q3	5.1031
95-th percentile	65.2302
Maximum	179.989
Range	359.989
Interquartile range (IQR)	14.8095

Descriptive statistics

Standard deviation	54.25579163
Coefficient of variation (CV)	-5.568465787
Kurtosis	3.610273321
Mean	-9.743400374
Median Absolute Deviation (MAD)	6.6907
Skewness	-0.02946184842
Sum	-703054.5408
Variance	2943.690926
Monotonicity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0	43	0.1%
0.2362	32	< 0.1%
0.2142	32	< 0.1%
3.8672	32	< 0.1%
2.4115	31	< 0.1%
3.4497	30	< 0.1%
3.8782	30	< 0.1%
-1.3788	30	< 0.1%
0.3186	30	< 0.1%
3.4222	29	< 0.1%
Other values (20258)	71838	99.6%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
-180	8	< 0.1%
-179.989	1	< 0.1%
-179.967	1	< 0.1%
-179.9561	1	< 0.1%
-179.9396	1	< 0.1%
-179.9341	1	< 0.1%
-179.9121	1	< 0.1%
-179.9066	2	< 0.1%
-179.8901	2	< 0.1%
-179.8462	1	< 0.1%

Value	Count	Frequency (%)
179.989	1	< 0.1%
179.9835	1	< 0.1%
179.978	1	< 0.1%
179.9561	1	< 0.1%
179.9066	1	< 0.1%
179.9011	1	< 0.1%
179.8132	1	< 0.1%
179.7913	2	< 0.1%
179.7089	1	< 0.1%
179.6759	1	< 0.1%

x10
Real number (ℝ_≥0)

HIGH CORRELATION

Distinct	1472
Distinct (%)	2.0%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%
Mean	34.45050733

Minimum	28.6121
Maximum	38.8919
Zeros	0
Zeros (%)	0.0%
Negative	0
Negative (%)	0.0%
Memory size	563.9 KiB

Quantile statistics

Minimum	28.6121
5-th percentile	29.5445
Q1	32.4475
median	35.1417
Q3	36.1476
95-th percentile	38.3065
Maximum	38.8919
Range	10.2798
Interquartile range (IQR)	3.7001

Descriptive statistics

Standard deviation	2.702819651
Coefficient of variation (CV)	0.07845514799
Kurtosis	-0.8898367712
Mean	34.45050733
Median Absolute Deviation (MAD)	2.3265
Skewness	-0.3010593016
Sum	2485845.257
Variance	7.305234064
Monotonicity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
31.5828	306	0.4%
31.5856	305	0.4%
36.1447	296	0.4%
31.5798	287	0.4%
36.1388	276	0.4%
31.5886	276	0.4%
29.9915	259	0.4%
36.1418	258	0.4%
31.5769	257	0.4%
31.5916	252	0.3%
Other values (1462)	69385	96.2%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
28.6121	1	< 0.1%
28.615	1	< 0.1%
28.6179	4	< 0.1%
28.6209	6	< 0.1%
28.6238	8	< 0.1%
28.6268	9	< 0.1%
28.6297	13	< 0.1%
28.6327	23	< 0.1%
28.6356	22	< 0.1%
28.6385	18	< 0.1%

Value	Count	Frequency (%)
38.8919	2	< 0.1%
38.8889	1	< 0.1%
38.883	3	< 0.1%
38.8801	10	< 0.1%
38.8771	11	< 0.1%
38.8742	22	< 0.1%
38.8713	26	< 0.1%
38.8683	34	< 0.1%
38.8654	41	0.1%
38.8624	53	0.1%

Spearman's ρ

The Spearman's rank correlation coefficient (ρ) is a measure of monotonic correlation between two variables, and is therefore better in catching nonlinear monotonic correlations than Pearson's r. It's value lies between -1 and +1, -1 indicating total negative monotonic correlation, 0 indicating no monotonic correlation and 1 indicating total positive monotonic correlation.

To calculate ρ for two variables X and Y, one divides the covariance of the rank variables of X and Y by the product of their standard deviations.

Pearson's r

The Pearson's correlation coefficient (r) is a measure of linear correlation between two variables. It's value lies between -1 and +1, -1 indicating total negative linear correlation, 0 indicating no linear correlation and 1 indicating total positive linear correlation. Furthermore, r is invariant under separate changes in location and scale of the two variables, implying that for a linear function the angle to the x-axis does not affect r.

To calculate r for two variables X and Y, one divides the covariance of X and Y by the product of their standard deviations.

Kendall's τ

Similarly to Spearman's rank correlation coefficient, the Kendall rank correlation coefficient (τ) measures ordinal association between two variables. It's value lies between -1 and +1, -1 indicating total negative correlation, 0 indicating no correlation and 1 indicating total positive correlation.

To calculate τ for two variables X and Y, one determines the number of concordant and discordant pairs of observations. τ is given by the number of concordant pairs minus the discordant pairs divided by the total number of pairs.

Phik (φk)

Phik (φk) is a new and practical correlation coefficient that works consistently between categorical, ordinal and interval variables, captures non-linear dependency and reverts to the Pearson correlation coefficient in case of a bivariate normal input distribution. There is extensive documentation available here.

Count
Matrix

A simple visualization of nullity by column.

Nullity matrix is a data-dense display which lets you quickly visually pick out patterns in data completion.

First rows

	x1	x2	x3	x4	x5	x6	x7	x8	x9	x10
0	0.2129	-0.7217	1.6621	10.9253	23.0713	-8.6670	-34.5081	-8.3386	-1.0931	33.8534
1	0.2188	-0.6841	1.7085	8.5449	24.7803	-6.6528	-34.3927	-8.1683	-1.2854	33.8564
2	0.2300	-0.6777	1.7251	0.1831	24.2310	-6.4697	-34.3652	-8.0035	-1.4777	33.8652
3	0.2358	-0.7075	1.6978	-9.2773	21.4844	-6.8359	-34.4312	-7.8662	-1.6589	33.8564
4	0.2378	-0.7476	1.6519	-12.8784	19.2261	-6.8359	-34.5355	-7.7454	-1.8237	33.8534
5	0.2227	-0.7661	1.6191	-9.6436	18.9819	-5.9204	-34.6124	-7.6245	-1.9830	33.8623
6	0.1929	-0.7725	1.6060	-4.9438	19.6533	-4.8218	-34.6399	-7.4927	-2.1368	33.8711
7	0.1660	-0.7778	1.6045	-2.6245	19.5923	-4.5166	-34.6509	-7.3553	-2.2852	33.8534
8	0.1528	-0.7896	1.6035	-2.1362	19.2261	-5.0659	-34.6509	-7.2235	-2.4390	33.8534
9	0.1523	-0.7905	1.6089	-1.4648	19.3481	-5.6152	-34.6454	-7.0972	-2.5983	33.8593

Last rows

	x1	x2	x3	x4	x5	x6	x7	x8	x9	x10
72147	0.2461	-0.3711	1.6851	252.8687	-81.2378	37.4146	-39.5288	65.2423	-65.3961	35.4594
72148	0.0918	-0.2065	1.6792	282.4707	-49.8047	40.3442	-35.3375	65.1160	-63.8910	35.4594
72149	0.0200	-0.0542	1.6909	270.3857	-46.6309	43.6401	-31.2891	64.9841	-62.4078	35.4476
72150	-0.0044	0.1348	1.7095	185.2417	-35.2173	34.4238	-28.4106	64.8633	-61.2762	35.4388
72151	-0.0742	0.2271	1.7188	80.2612	-10.1318	36.3159	-26.8286	64.9457	-60.4138	35.4447
72152	-0.0605	0.2568	1.7686	27.9541	18.6157	3.4790	-26.6583	65.1270	-60.5402	35.4594
72153	-0.0293	0.3091	1.8848	32.5317	55.9082	-48.8281	-27.8174	65.4071	-62.1716	35.4711
72154	-0.0313	0.3633	2.0269	72.6929	60.1196	-56.8237	-28.8007	65.6763	-64.0558	35.4653
72155	-0.0479	0.4219	2.1865	126.4648	21.5454	-28.4424	-28.3173	65.7257	-64.9127	35.4505
72156	-0.0391	0.4165	2.4741	179.4434	-19.5313	-4.2725	-26.4001	65.5334	-64.7754	35.4535

Most frequently occurring

	x1	x2	x3	x4	x5	x6	x7	x8	x9	x10	# duplicates
0	-0.038989	0.236694	0.812228	0.316112	0.502639	0.044121	22.463468	0.87089	-9.7434	34.450507	3

Overview

Variables

Interactions

Correlations

Spearman's ρ

Pearson's r

Kendall's τ

Phik (φk)

Missing values

Sample

First rows

Last rows

Duplicate rows

Most frequently occurring